What a pity it's a trap...
Homer Simpson is hardly like a man who is able to intervene in one of the most famous mathematical disputes in history. But in the series “The Wizard of Evergreen Terrace”, the authors of the “Simpsons” hid a formula on the board that at first glance does the impossible: as if refuted the great theorem of Fermat. Some could have imagined that there was no nonsense on the board (this is just a cartoon), but behind a few figures there is a real story longer than 350 years.
The series was released in 1998. In the story, Homer is experiencing a midlife crisis and painfully compares his own life with the biography of Thomas Edison. The inventor left behind a filament lamp, a phonograph and many patents, and Homer... Well, we know. Therefore, he decides to become the new Edison, locks himself in the basement and begins to invent his own great inventions.
In one of the frames, Homer stands in front of a painted board. Next to the doughnut sketches there is a strange equality: 398712 + 436512 = 447212. For most viewers, this is just a set of large numbers and degrees. But the mathematician immediately sees the problem: if equality was true, it would destroy one of the most famous theorems in mathematics.
To understand what the point is, you need to start with a simple recording: xn + yn = zn. At n = 1 everything works without special conditions. You can take any positive whole x and y, fold them and get a positive whole z. For example, 3 + 6 = 9.
At n = 2, we get a formula familiar by school geometry: x2 + y2 = z2. This is how the Pythagoras theorem is recorded. It describes a rectangular triangle, where the sum of the squares of the two cathetes is equal to the square of the hypotenuse. But even here whole x and y do not always give a whole z. If you take 1 and 2, you get 12 + 22 = 5. The number 5 is not a square of the whole number, which means that the length of the hypotenuse will not be integer.
Then the main intrigue begins. At n = 3, you need to find three positive integers that perform equality x3 + y3 = z3. In ordinary language, the task is as follows: is it possible to fold the volumes of two cubes with whole ribs and get the volume of the third cube, which also has a whole rib? Fermat's great theorem says it is impossible. The same is true for any degree more than 2.
Pierre de Fermat noticed this pattern in the XVII century. The French mathematician wrote on the margins of Diophantus of Alexandria that he found evidence: the equation xn + yn = zn has no solutions in positive integers, if n more than 2. The very proof of the Farm did not leave. Later, mathematicians analyzed almost all his similar notes, but it was this task that lasted longer than others and entrenched in history.
For more than 350 years, mathematicians have been trying to close this gap. The decision came out only in 1994, when the British mathematician Andrew Wiles completed the proof. He had to go far beyond the school algebra. Wiles did not pick up the numbers and did not try to directly sort all the options for x, y and z. The proof was based on elliptical curves and modular forms: complex sections of mathematics that bind equations, geometry, and symmetries. The desired apparatus appeared only in the 20th century, so the Farm in the XVII century could not reason with the same language. Because of this, the old mark in the fields still leaves the question: the Farm made a mistake, joked, overestimated his idea or did he really see a simpler path that no one later regained?
Wiles’s work was checked especially carefully. The evidence used new methods, and the methods themselves then returned to mathematics more than once and helped to find other connections between complex objects. Therefore, trust in the result is maintained not only on the authority of the author, but also on the long-term verification of his approach by specialists. In 2016, Wiles received the Abel Prize, one of the main awards in mathematics. For the history of the Homer board, this means a simple thing: the real solution of the equation xn + yry = zn in positive integers at n more than 2 should not be.
That's why the recording on the Houseboard is so funny. In equality 398712 + 436512 = 447212 degree is 12, which means that the formula falls directly under the prohibition of the Fermat theorem. All three numbers are integer, the record looks neat, and the usual calculator even shows that the left and right sides coincide. The catch is hidden not in the theorem, but in rounding. The numbers of the species 398712, 436512 and 447212 are huge: in the calculations, values appear about 44 digits. Household calculator usually shows only the first 10 digits and discards the rest. Due to rounding, two different sizes look the same. A more accurate computer calculation immediately shows that 398712 + 436512 is not equal to 447212.
The authors of the “Simpsons” derived this formula not by chance. Among the writers of the series there were many people who made things sense in mathematics, physics and computer science. David Cohen was responsible for a joke with Fermat's theorist. He specifically wrote a program that was looking for almost coincident meanings. A formula was needed that did not violate mathematical laws and deceiving the usual calculator well enough.
The Theorem of Fermat was also not accidental. During his studies, Cohen listened to lectures by mathematician Ken Ribet, whose work helped prepare the evidence for Wiles. So the House of Homer is a precisely collected mathematical Easter.
Homer Simpson is hardly like a man who is able to intervene in one of the most famous mathematical disputes in history. But in the series “The Wizard of Evergreen Terrace”, the authors of the “Simpsons” hid a formula on the board that at first glance does the impossible: as if refuted the great theorem of Fermat. Some could have imagined that there was no nonsense on the board (this is just a cartoon), but behind a few figures there is a real story longer than 350 years.
The series was released in 1998. In the story, Homer is experiencing a midlife crisis and painfully compares his own life with the biography of Thomas Edison. The inventor left behind a filament lamp, a phonograph and many patents, and Homer... Well, we know. Therefore, he decides to become the new Edison, locks himself in the basement and begins to invent his own great inventions.
In one of the frames, Homer stands in front of a painted board. Next to the doughnut sketches there is a strange equality: 398712 + 436512 = 447212. For most viewers, this is just a set of large numbers and degrees. But the mathematician immediately sees the problem: if equality was true, it would destroy one of the most famous theorems in mathematics.
To understand what the point is, you need to start with a simple recording: xn + yn = zn. At n = 1 everything works without special conditions. You can take any positive whole x and y, fold them and get a positive whole z. For example, 3 + 6 = 9.
At n = 2, we get a formula familiar by school geometry: x2 + y2 = z2. This is how the Pythagoras theorem is recorded. It describes a rectangular triangle, where the sum of the squares of the two cathetes is equal to the square of the hypotenuse. But even here whole x and y do not always give a whole z. If you take 1 and 2, you get 12 + 22 = 5. The number 5 is not a square of the whole number, which means that the length of the hypotenuse will not be integer.
Then the main intrigue begins. At n = 3, you need to find three positive integers that perform equality x3 + y3 = z3. In ordinary language, the task is as follows: is it possible to fold the volumes of two cubes with whole ribs and get the volume of the third cube, which also has a whole rib? Fermat's great theorem says it is impossible. The same is true for any degree more than 2.
Pierre de Fermat noticed this pattern in the XVII century. The French mathematician wrote on the margins of Diophantus of Alexandria that he found evidence: the equation xn + yn = zn has no solutions in positive integers, if n more than 2. The very proof of the Farm did not leave. Later, mathematicians analyzed almost all his similar notes, but it was this task that lasted longer than others and entrenched in history.
For more than 350 years, mathematicians have been trying to close this gap. The decision came out only in 1994, when the British mathematician Andrew Wiles completed the proof. He had to go far beyond the school algebra. Wiles did not pick up the numbers and did not try to directly sort all the options for x, y and z. The proof was based on elliptical curves and modular forms: complex sections of mathematics that bind equations, geometry, and symmetries. The desired apparatus appeared only in the 20th century, so the Farm in the XVII century could not reason with the same language. Because of this, the old mark in the fields still leaves the question: the Farm made a mistake, joked, overestimated his idea or did he really see a simpler path that no one later regained?
Wiles’s work was checked especially carefully. The evidence used new methods, and the methods themselves then returned to mathematics more than once and helped to find other connections between complex objects. Therefore, trust in the result is maintained not only on the authority of the author, but also on the long-term verification of his approach by specialists. In 2016, Wiles received the Abel Prize, one of the main awards in mathematics. For the history of the Homer board, this means a simple thing: the real solution of the equation xn + yry = zn in positive integers at n more than 2 should not be.
That's why the recording on the Houseboard is so funny. In equality 398712 + 436512 = 447212 degree is 12, which means that the formula falls directly under the prohibition of the Fermat theorem. All three numbers are integer, the record looks neat, and the usual calculator even shows that the left and right sides coincide. The catch is hidden not in the theorem, but in rounding. The numbers of the species 398712, 436512 and 447212 are huge: in the calculations, values appear about 44 digits. Household calculator usually shows only the first 10 digits and discards the rest. Due to rounding, two different sizes look the same. A more accurate computer calculation immediately shows that 398712 + 436512 is not equal to 447212.
The authors of the “Simpsons” derived this formula not by chance. Among the writers of the series there were many people who made things sense in mathematics, physics and computer science. David Cohen was responsible for a joke with Fermat's theorist. He specifically wrote a program that was looking for almost coincident meanings. A formula was needed that did not violate mathematical laws and deceiving the usual calculator well enough.
The Theorem of Fermat was also not accidental. During his studies, Cohen listened to lectures by mathematician Ken Ribet, whose work helped prepare the evidence for Wiles. So the House of Homer is a precisely collected mathematical Easter.
